Three-dimensional symmetry breaking topological matters

Abstract

We discuss topological electronic states described by the Dirac Hamiltonian plus an additional one in three-dimension. When the additional Hamiltonian is an element of an Abelian group, electronic states become topologically nontrivial even in the absence of fundamental symmetries such as the time-reversal and the particle-hole symmety. The symmetry-breaking topological states are charercterized by the Chern number defined in the two-dimensional partial Brillouin zone. The topological insulators under Zeeman field are an example of the symmetry-breaking topological matters. We show the transision from the topological insulating phase to the topological semimetal one under the strong Zeeman field.

5 pages, 4 figures

References in corpus (8)

• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Crystalline Insulators
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B
• Interface Metallic States between a Topological Insulator and a Ferromagnetic Insulator

Cited by in corpus (5)

• Dynamical conductivity in topological nodal-line semimetal ZrSiS
• Three-dimensional graphdiyne as a topological nodal-line semimetal
• Tunneling Conductance in a Two-dimensional Dirac Semimetal Protected by Non-symmorphic Symmetry
• Transport in a thin topological insulator with potential and magnetic barriers
• Electric polarization in magnetic topological nodal semimetal thin films